The former Romanian No.10, who now owns Viitorul Constanta, hopes that the Istanbul club can be restored to the pinnacle of the continental football
Hagi won 10 titles, including the Uefa Cup, during his playing days in Istanbul, led the club to the Turkish Cup as coach in 2005, and returned to the helm for one year in 2010.
And while he admitted that he no longer takes as much of an interest as he used to, he hopes that Terim can build on last season's Super Lig triumph.
"I only watched a few Galatasaray matches, not much. For now they are in a transitional process. They want to assemble a team that wants to win," the Romanian told GSTV.
"That is Fatih Terim's project and that is Galatasaray's identity. Once more, Galatasaray must triumph in Europe," he continued.
Hagi also gave his opinion on the Istanbul giants' star men.
"Selcuk Inan has qualities, he's a fine player and has character," he said.
"Emre Colak is more like me. But he is very young and needs to get experience."
The Romanian, who donned the No.10 shirt for Cimbom, spoke of the importance of this type of player.
"Selcuk is very talented but needs a No.10 in front of him. In the Galatasaray team, there is always a No.10 player and he must make the difference," Hagi said.
Even though he wishes his former team to be successful in Europe again, the Viitorul Constanta owner knows that he must look at things realistically.
"Fatih Terim knows what he has to demand [from his team]. They must be successful in Europe, step by step," he declared.
"But for now, this is far more difficult. We hope to see Galatasaray in Europe again, like back in those days [when he was a player]," he admitted.
The Romanian star also offered his opinion on possible transfer targets that could help restore the club to its former glory.
"I know Umut Bulut and Dany and I think they are decent players for Galatasaray. But Terim knows this better.
"I wholeheartedly want Galatasaray to be strong. Galatasaray are a European team. I wish Terim and my old friends there all the best," Hagi concluded.